Stuttering is a neurological problem where the brain does not process the speaker's voice properly as s/he speaks. When you do not use your own voice the stuttering is usually markedly decreased. This is why we speak better when we whisper, sing, speak in a flsetto or speak in unison. One thing you can try is to whisper or sing or use a falsetto voice. Another option is to obtain a speech prosthesis which will mask your voice and/or let you hear your voice a split second after you speak.